1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find La Placian of a function in cartesian and Spherical Coordinates

  1. Feb 16, 2013 #1
    1. The problem statement, all variables and given/known data
    Prove the La Placian of V(x,y,z)=(zx[itex]^{2}[/itex])/(x[itex]^{2}[/itex]+y[itex]^{2}[/itex]+z[itex]^{2}[/itex]) in Cartesian coordinates is equal to that in Spherical coordinates


    2. Relevant equations

    [itex]\nabla[/itex][itex]^{2}[/itex]V=0


    3. The attempt at a solution

    I have attempted to calculate all the terms out, and there were A LOT. I was hoping the derivatives in Cartesian, which I did first, would cancel, but they didn't. I may have made a mistake, I used the product rule and came up with 6 terms in the numerator over (x[itex]^{2}[/itex]+y[itex]^{2}[/itex]+z[itex]^{2}[/itex])[itex]^{3}[/itex]. Any suggestions? Spherical was even more complicated... I had the following:
    r(cosθ)[itex]^{2}[/itex](sin[itex]\phi[/itex])[itex]^{2}[/itex](cos[itex]\phi[/itex]) before I began taking partial derivatives. Any help would really be appreciated, thanks...
     
    Last edited: Feb 16, 2013
  2. jcsd
  3. Feb 17, 2013 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Re: Find La Placian of a function in cartesian and Spherical Coordinat

    Which convention for spherical coordinates are you using? Physicists typically use ##\theta## as the angle from the z-axis whereas mathematicians use ##\phi##. Your expression for ##V(r,\theta,\phi)## appears to be using the math convention. I just ask because you posted this in the physics section.

    No suggestions, by the way. I think you just have to grind it out.
     
  4. Feb 17, 2013 #3
    Re: Find La Placian of a function in cartesian and Spherical Coordinat

    This problem is from a physics class, and the class doesn't have a book assigned...so I've been looking through my calc iv book to try and get some information. Thanks for pointing out there are different systems, I wasn't aware of that and my professor didn't mention it...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find La Placian of a function in cartesian and Spherical Coordinates
  1. Spherical coordinates (Replies: 3)

Loading...